# Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification

arXiv: https://arxiv.org/abs/2610.19351 · HTML: https://mlsanity.com/paper/2610.19351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [A Statistical Perspective on Algorithmic Leveraging](https://mlsanity.com/paper/1306.5362/) (2013)
- [Optimal Subsampling for Large Sample Logistic Regression](https://mlsanity.com/paper/1702.01166/) (2017)
- [Local case-control sampling: Efficient subsampling in imbalanced data sets](https://mlsanity.com/paper/1306.3706/) (2013)
- [Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators with Massive Data](https://mlsanity.com/paper/2005.10435/) (2020)
- [Information-Based Optimal Subdata Selection for Big Data Linear Regression](https://mlsanity.com/paper/1710.10382/) (2017)
- [Optimal Subsampling Algorithms for Big Data Regressions](https://mlsanity.com/paper/1806.06761/) (2018)
- [Optimal subsampling for quantile regression in big data](https://mlsanity.com/paper/2001.10168/) (2020)
- [Orthogonal Subsampling for Big Data Linear Regression](https://mlsanity.com/paper/2105.14647/) (2021)
- [LowCon: A design-based subsampling approach in a misspecified linear modeL](https://mlsanity.com/paper/2010.12178/) (2020)
- [Signal Representations on Graphs: Tools and Applications](https://mlsanity.com/paper/1512.05406/) (2015)
- [A First-Order Algorithm for the A-Optimal Experimental Design Problem: A Mathematical Programming Approach](https://mlsanity.com/paper/1311.2335/) (2013)
- [Scalable Resampling in Massive Generalized Linear Models via Subsampled Residual Bootstrap](https://mlsanity.com/paper/2307.07068/) (2023)

## Abstract (arXiv)

In many modern applications, obtaining response variables is costly, time-consuming, or technically challenging, making it impractical to measure outcomes for all available units. In such settings, covariates may be available for a large pool of candidates, but responses can only be collected for a small, carefully selected subset, making the choice of which units to measure a consequential decision. Most existing subsampling methods are developed for massive datasets, emphasizing the trade-off between statistical accuracy and computational cost, and typically relying on the assumption of a correctly specified model. These features limit their suitability in measurement-constrained settings, where statistical efficiency is paramount and model misspecification is often unavoidable. To address these challenges, we develop a new subset selection framework for linear regression that accommodates potential model misspecification. The proposed approach targets predictive expected loss and yields an A-optimality-type criterion that depends only on covariate information, requiring no response observations at the selection stage. We refer to this method as Expected Loss Optimal Selection (ELOS). By focusing on predictive risk rather than model-based optimality, ELOS remains well-defined and robust under misspecification. Simulation studies and real data applications demonstrate that ELOS achieves strong predictive performance and compares favorably with existing methods across a range of scenarios.